Activation entropy definition

While all of these experimental facts seem to strongly suggest the intermediate existence of a thianorcaradiene, more definitive evidence might be obtained by a kinetic study of the stable monocyclic thiepin 101 for which a large negative activation entropy is to be expected. We are currently investigating this point. 

Analysis of the transition state in terms of energy is certainly a key aspect of the S 2-ET problem. Entropy considerations may, however, bring about additional information, possibly helping us to conceive better the transition between the two mechanisms. It was observed in this connection that, whereas the entropy of activation of both the anthracene anion radical and of the ETIOPFe(O) porphyrin (pp. 99, 100) (which have about the same standard potential) is close to zero in their reaction with s- and t-butyl bromides a definitely negative value, ca. — 20 eu is obtained for the reaction of the porphyrin with n-butyl bromide (Lexa et al., 1988). The same was found for the reaction of two other iron porphyrins, TPPFe(o) and OEP-Fe(i). These activation entropies were estimated from (153), where Z is... 

In a Markov first-order process, the six possible ratios of rate constants can be calculated according to Equations 7-12 if the three triad fractions Xu, Xi8, and X88 are known. We thus get six differences of activation enthalpies and activation entropies. Only two of them, however, are really independent because by definition ... 

Entropy is a sophisticated concept, and this is not the place to give a rigorous definition of disorder suffice it to say that a disordered system is more probable than an ordered one, and the entropy ofa system is proportional to the logarithm ofits probability [101]. Intuitively, we see that A5 > 0 for a process in which the product orthe transition state is less symmetrical or has more freedom of motion than do the reactants. For example, ring-opening reactions, since they relieve constraints on intramolecular motion, should be accompanied by an increase in entropy. Note that an increase in entropy favors a process it increases a rate constant (activation entropy) or an equilibrium constant (reaction entropy), while an increase in enthalpy disfavors a process. 

A. Definitions and Interrelations of Activation Free Energy, Activation Heat, and Activation Entropy of Steady Reaction... 

Thus, the steric factor may be explained with the help of entropy change. When two molecules come together to produce the activated complex, the total translational degrees of freedom are reduced (from 6 to 3) and rotational degrees of freedom also diminish. This is compensated by an increase in vibrational degrees of freedom. But the definite orientation in forming the activated complex necessarily reduced the entropy, i.e. AS is negative. This decrease in entropy is small when reaction takes place between simple atoms. The calculated value of kbT/h corresponds to collision frequency... 

The same models as for intermolccular processes are applied for intramolecular diastereoface differentiating double-bond additions. However, there are some advantages in the intramolecular version. Firstly, the entropy factor lowers the barrier of activation and allows reactions to proceed at lower temperatures, which increases the selectivity. Secondly, the cyclic transition states introduce the elements of ring strain and transannular interactions, which lead to enhanced differences between two diastereomorphous geometries. Both of these factors cooperate to increase the selectivity of the intramolecular reaction. For example, halolactonization, by definition, is an intramolecular process. 

In the first and second equation, E is the energy of activation. In the first equation A is the so-called frequency factor. In the second equation AS is the entropy of activation, the interatomic distance between diffusion sites, k Boltzmann s constant, and h Planck s constant. In the second equation the frequency factor A is expressed by means of the universal constants X2 and the temperature independent factor eAS /R. For our purposes AS determines which fraction of ions or atoms with a definite energy pass over the energy barrier for reaction. 

In an earlier section the free energy of a phase and the free energy of a total system were discussed generally in terms of the potentials (e.g., equation 48). With the definition of the chemical potential as a function of activity in hand, we will now consider the Gibbs energy of a system. In a similar fashion, the enthalpy and entropy of a system can be computed using the partial molar quantities and the mole numbers of each phase. 

Although Dahn and Gold accepted Lane and Feller s diagnosis of the mechanism in acetic acid, they argued that a change of mechanism occurs in the more polar aqueous medium with its weaker nucleophiles (water as opposed to acetate), and that reaction of the diazonium ion is now unimolecular. The more positive entropy of activation and the correlation with Hammett s acidity function were cited in support of their view. However, neither of these criteria can now be considered definitive, and the most striking fact is the similarity of the results to those for diazoacetic ester. Careful application of the Swain-Soott relation would appear to provide the best criterion of the molecularity of nitrogen loss, but at present suitable results are not available. 

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